Automatic computing apparatus



Dec. 1, 1959 Filed Jfine 2, 1953 HENRI-GEORGES DOLL 4 Sheets-Sheet -1 BIASED ELECTRONIC 'NTEGRATOR AMPLIFIER swITcH 32 I so INTEGRATOR B'ASED ELEOTRONC AMPLIFIER SWITCH '1 4s 45 35 3e 37 J PHASE AMPLIFIER OUTPUT INVERTER DEVICE 52 I 8 f. c 1 l I INVENTOR.

HENRI-GEORGES DOLL HIS ATTORNEY Dec. 1, 1959 HENRI-GEORGES DOLL 2,915,242

AUTOMATIC COMPUTING APPARATUS 4 Sheets-Sheet 2 Filed June 2, 1953 BIASED AMPLIFIER OUTPUT DEVICE BIASED AMPLIFIER FIG] b 2 b 3 4 R R. m cm A EF R U m up I. T BM a N A I 9 8 2 A w R R m 4 E A EF 1 R L m mw T N A v I? n I a l 8 3v 3 8 INVENTOR.

HENRFGEORGES DOLL HIS ATTORNEY FIG.8

V1959 HENRI-GEORGES DOLL 2,915,242

AUTOMATIC COMPUTING APPARATUS Filed June 2. 195:5

4 Sheets-Sheet 3 1 swee GENERATOR m 4 G 2 w W 1 m 3 E E E/MN. 2 w m OUTPUT COMBINING DEVICE :iINTEGRATOR PULSE EQUALIZER FIG.9

I FIG." i

VARIABLE GAIN AMPLIFIER k} I59 VARIABLE GAIN AMPLIFIER SWEEP. GENERATOR FIGJO INVEN TOR.

HENRI-GEORGES DOLL FIG l2 HIS ATTORNEY This invention relates to automatic computing apparatus and, more particularly, pertains to an improved computer of the type providing a signal continuouslyrepresentative of the value of a specified function'of a plurality of independent variables supplied thereto.

In the copending application of H. G. Doll, -filed J uly- 1,' 1952, hearing the Serial Number 296,675, now Patent No. 2,829,825, there is described one form of apparatus of the above-stated type. According to that disclosure, a predetermined function of two independent variables is plotted on a screen in terms of-abrupt changes in light transmission coefiicient. There is thus provided a family of curves, each curve corresponding to 'z=f(x, y) fora particular value of z, the dependent variable. A beam of light is positioned at some point along a linear path on the screen in accordance with the instantaneous value of one independent variable, x, and the screen is' continuously displaced in a direction perpendicular to the aforesaid linear path- .The number of curves that intercept the light beam in a time interval determined by the instantaneous value of the'remaining of the independent variables, y, is indicative of'the instantaneous value of dependent variable 2. ."e

Anothercomputer of the general type under consideration is disclosed in the copending application of H. G. Doll, filed June 2, 1953, bearing the Serial Number 359,197, now Patent No. 2,859,916, and entitled Automatic Computing Apparatus." In that computer, a screen inscribedwith a family of curves is positioned adjacent the fluorescent screen of a cathode ray tube and a line sweep of essentially fixed length and direction is developed on the fluorescent screen. Each time the sweep trace intercepts a curve line, a light impulse is generated and the sweep trace is continuously oriented relative to, a reference coordinate system in accordance with instantaneous values of independent variables xand y. The lightflpulsesrepresentingthe number of curves interceped by the sweep traceare counted thereby deriving the instantaneous value of dependent variable z.

These systems are generally satisfactory for a great many functions. However, they may .not afford accurate computations for functions in which a particular value 25 of z=f(x, y), may be obtained for two or more values of the same independent variable in the region of interest, e.g., if the light beam or sweep trace intercepts the same curve or curves more than once. 7

It is, therefore, an object of the present invention to elfectcertain improvements inthe apparatus described in the aforementioned Doll applications.

Another obiect of the present invention is to provide animproved automatic computer capable of accommodatingfunctions of two independent variables in which a particular solution exists. for two or more valuesof one of the independentvariables, but providing that so-.

lution-for one value of the one variable dictated by the value of the other of the independent variables. In a computer of either of the above-described form there is usually included a counter for summing the rated. D

.- 1 2 not:

pulses corresponding to'th 'n terceptions of afnumber. of curves in the family by ,the light beam 'orsweepv trace; The counter develops a pptential'representingthat num-. ber supplied to an indicator, such as aivoltmeter. L,This-, circuit responds to absolute numbers offpulses, iter, all

pulses are equally weighed. Thuspthe familvofi curves k and a compensatingpotential l must be considered as liavingyalues ofthesame sign, either all positive or all negatiye If the curves, have; actual, Values of t w resand ne a ive sig the curves are assigned consecutive values of.the same sign; t q uq s ea e volt meter which is calibrated: toindicate values, of both posi-; livs and negative n- .T i .t l .somp s t o t course, must be efiected-ieachgtime a difierent functitim, or the same function with a difierent range of values, is accommodated byvexchanging curvefamiliesy v A 1 Thus, it another object of thepresent invention to: provide ,an, improved automatic computer capable I of accommodating a family of curves having valuesof both positive and negative sign. i I

A further object of the present inven 1 'is to provide an improved: automatic computertor. util zing a family of curves exhibiting values of both positive and negative sign wherein no adjustment is. requiredtonany of various families of curves.- I Q An automatic computing apparatus according to the present invention comprises a family of curves occurring in two groups defined bya referenceline and.meanstor. projecting radiant energy toward the curves. i and the radiant energy are recur rently. and relativelysdisplaced to effect modulation of theira'di-ant energy. Means are provided for deriving respective, electrical signals, each representing one of the twogroupsiof curves. The electrical signals arev suitablyl combined so .as toidetermine the instantaneous value-of the dependent variable In accordance with one embodiment oftheinvent om there is provided a screen on which the curve groups are plotted. At least one beam of light is'project'ed' toward;

the screen and the beam and the screen are displaced relative to one another periodically to scan thetwocurvegroups. The referencelinedet ermining the two groups, of curves isthe locus of the pointsjofjtan'gency' between the several curves and corresponding lines o fiscani"; The.

relative positions of the screen ,a'nd the pointlofimpingvment of'the'light beam on thescreenarejmodified in a direction angularly disposed to the direction of scan according to the instantaneousyalueof one independent variable and means are provided; for inter;eptiriglight energy after modification by thecurves and'for deriving" an individual pulse-typeisignalfoneach curve group. A

number of pulses in eachofith'ese signals is selected in, accordance with the instantaneous v'alueiof the other independent variable and the selected pulses of the two signals arecombined to determine the instantaneous value of the dependent variable.

ance with instantaneous values of the independent yartables. and means are provided for deriving electrical sig' -Q naljsg, each. corresponding to the radiant energy modified; by oneofthe curve groups.. These electricalsignals 1',

combined to determine the instantaneous value of dependent variables p r a In yet another embodiment ofthe invention, which may be generally like either of the above embodiments the family ofc'urves exhibits values of positive and negative The curves sign and the two curve groups are defined by a reference line separating these values.

The novel features of the present invention are set forth with particularity in the appended claims. The present invention, both as to its organization and manner of operation together with further objects and advantages thereof, may-best be understood by reference to the following description taken in connection with the accompanying drawings in which:

Fig; l is a schematic diagram, partly in block form, of an automatic computing apparatus constructed in accordance with the present invention;

Fig. 2 represents a family of curves for a particular function of two independent variables, such as may be accommodated by the apparatus of Fig. 1, and employed as illustrative of the operation of the apparatus;

Fig. 3 represents various waveforms useful in explaining the operation of the apparatus shown in Fig. 1;

Figs. 4 and 5 are families of curves illustrating various other functions of two independent variables that may be accommodated by the computing apparatus of Fig. 1;

Figs. 6, 7 and 8 represent modifications of the apparatus shown in Fig. 1;

Fig. 9 is a perspective view of another embodiment of the present invention;

Figs. 10 and, 11 are modifications of the apparatus shown in Fig 9;

Fig. 12 illustrates the manner of treating a representative family of curves for application to the apparatus of Fig. 11;

Fig. 13 represents a family of curves which may be accommodated by another embodiment of the present invention; and

Figs. 14 and 15 illustrate, schematically, respective forms of that embodiment.

In Fig. 1 of the drawings, there is illustrated a computer constructed in accordance with the present invention and embodying features disclosed and claimed in the aforementioned copending Doll application Serial Number 296,675, now Patent No. 2,829,825. This computer comprises a movable screen in the form of a transparent, endless belt 10 provided with sprocket holes 11 in meshing engagement with sprocket wheels 12 and 13. Wheel 13 is rotated by a driving motor 14, preferably at a constant speed, thereby displacing the belt at a fixed velocity.

' Screen 10 is provided with opaque curves occurring in two alternating groups 15 and 16. With reference to Fig. 2, these groups correspond to portions 17 and 18, respectively 'of the family of curves there represented. The particular family of curves, used purely by way of example, represents the function of two independent vari ables expressed by the formula:

where his a constant. This is the familiar parabolic function with the foci of the several curves distributed along a line 19 parallel to the x-axis. Line 19 determines the extent of each of the curve groups 17 and 18 in the illustrated function. However, for the general case, dividing or reference line 19 may be defined as the locus of the points of 'tangency between lines parallel to the y-axis and the several curves. As will be described hereinafter, curve family 17, 18 is scanned by apparatus embodying the invention in a direction S, parallel to the y-axis.

As shown in Fig. l, the curve groups 15 and 16 are positioned in their respective frame portions 20 and 21 of belt 10 in the same relative positions as would occur if each pair of complementary groups were disposed in the same frame. That is, the curve groups 15 are positioned in the lower one-half of their frames 20 and the curve groups 16 are positioned in the upper one-half of their frames 21. I

Light energy from a source (not shown) isrefiected by a mirror galvanometer 22 and projected in a beam 23 toward, the section of belt 10 carrying curve groups 1.5

4 and 16. A voltage having a magnitude proportional to the instantaneous value of independent variable x is applied to galvanometer 22; thus, the position of beam 23 along a horizontal path on belt 10, perpendicular to its direction of movement, is dependent upon the value of variable x.

Since the belt moves continuously, the light beam 23 is modified or modulated by the opaque curves 15 and 16 and the modulated light energy is intercepted by an elongated photoelectric cell 24 disposed interiorly of belt 10. Consequently, the electrical output between conductors 25 extending from photocell 24 is dependent upon independent variable x; i.e., the time-spacing and/or position of output pulses at leads 25 are dependent upon the value of variable x. If the modulated output wave is integrated with respect to time limits determined by the instantaneous value of independent variable y, an instantaneous value of z is automatically obtained.

To that end, light energy is reflected in a beam 26 from another mirror galvanometer 27 to which is applied another voltage representing the instantaneous value of variable y. Beam 26 is positioned by this voltage along a horizontal path perpendicular to the direction of move ment of belt 10 relative to a consecutive series of opaque regions 28. Each of regions 28 is disposed in one of frames 20, 21 so that there is one laterally-adjacent opaque region for each of the curve groups 15 and 16. Photocell 24 also intercepts light beam 26, after its modulation by regions 28. Thus, at leads 25 of the photocell, rectangular pulses are derivedhaving durations dependent upon the instantaneous values of variable y.

The output pulses produced by photocell 24 in response to curve groups 15 and 16 and region 28 of belt 10 are supplied over leads 25 to the input circuits (not shown) of two electronic switches 29 and 30. These switches are operatively conditioned,: by means hereinafter described, in such a manner that switch 29 translates signals from photocell 24 only during intervals in which beam 23 is modulated by the curves of groups 15 and switch 30 translates signals from the photocell only during intervals in which beam 23 is modulated by the curves of groups 16. The output signals from electronic switches 29 and 30 are supplied to respective, biased or amplitude-selective amplifiers 31 and 32, in turn, coupled to individual integrators or pulse counters 33 and 34. The integrators are coupled to a combining network 35 comprised of a pair of series-connected resistors 36, 37 having their junction connected to oppositely-poled terminals of the integrators and their free ends connected to the remaining terminals. An output device 38, such as a recording voltmeter is coupled to the combiningnetwork 35.

In order to operate switches 29 and 30 in synchronism with movement of curve groups 15 and 16, belt 10 is provided with narrow, consecutive, synchronizing strips 39 and 40. Strips 39 are opaque and are individually.

disposed in one of frames 20, whereas strips 40 are transparent and are disposed in frames 21. Thus, the strips 39, 40 define a narrow, linear path along which they travel as belt 10 is displaced. Light energy from a source 41 is concentrated by a condensing lens 42 in a beam on this path and after modulation by strips 39, 40 the beam is intercepted by a photoelectric cell 43. The output leads '44 of cell 43 are connected to an amplifier 45 whose output leads are connected to the actuating portion (not shown) of electronic switch 29 and to a phase inverter 46. The phase inverter, in turn, is connected to the actuating portion (not shown) of electronic switch 30.

The operation of the system just-described may be best understood by reference to Fig. 3, which represents various waveforms of the system, plotted to a common time scale. For convenience of explanation, it is assumed that the photocells produce output potentials of positive polarity, relative to a plane of reference potential, in response to the interruption of incident light by .an opaque portion of belt 10.

Galvanometers 22 and 27 are supplied with individual voltages having magnitudes dependent upon the instantaneous values of independent variables x and y, respectively. Thus, light beams 23 and 26 are displaced by respective amounts according to these values.

As the curves 15 sweep past light beam 23, a series of short-duration pulses are generated by photocell 24. Simultaneously, a corresponding one of regions 28 modulates light beam 26 so that a rectangular pulse is generated by the photocell.

The short pulses such as 50 of Fig. 3, have a time spacing and distribution dependent upon the instantaneous value of variable x and may be in part concurrent with rectangular pulse 51 which has a duration dependent upon the value of variable y. Thus, the pulses in group 50, dependent upon both x and y, have an effective amplitude greater than the others in the group.

During the interval of the occurrence of pulses 50, 51, opaque strip 39 interruptsthe light beam directedltoward photocell '43 thereby producing a rectangular pulse, represented at 52 in Fig. 3. This pulse is amplified in stage 45 before being utilized for operatively conditioning switch 29. Consequently, pulses 50, 51 are supplied to biased amplifier 31 during an interval defined by pulse 52. Only those of the short pulses of effectively greatest amplitude are selected by the amplifier and supplied to integrator 33 for counting.

In the operating interval just considered, electronic switch 30 is disabled, however, in the next successive operating interval, a rectangular pulse 53 (Fig. 3) from phase inverter 46, corresponding in timing to transparent section 40 of the synchronizing strip, operatively conditions this switch, while switch 29 is disabled. Light beams 23 and 26, delineating the values of variables x and y in terms of their positions .on belt are modulated by the curves of group 16 and an adjacent region 28, respectively. The resulting output pulses from photocell 24 represented by short pulses 54 and rectangular pulse 55 in Fig. 3A, are supplied via switch 30 for amplitude selection in amplifier 32 before the selected ones of the short pulses are counted by integrator 34.

The foregoing two types of operating intervals occur in continuous, alternating relationship and two discrete pulse-type signals are applied to integrators 33 and 34. Each of these signals denotes pulse values for each of curve. family portions and 16 (portions 17 and 18 of Fig. 2).

The integrators produce voltages corresponding to the numbers of applied pulses and these voltages are subtractively combined in network 35. Hence, there is derived at network 35 a potential having a magnitude responsive to the instantaneous value of dependent variable 2. This potential is indicated by device 38.

It is thus evident that by considering the integrated quantities, responsive to curve groups 17 and 18, respectively, (Fig. 2) as of opposite polarity and then adding, accurate computations are possible even though for every value of x and each curve 2, there are two values of y. In other words, the curve groups 17 and 18 separated by reference line 19 are effectively given opposite senses and thereby distinguished from one another.

In Fig. 4 there is illustrated another type of two-valued function which may be accommodated by the justdescribed computer. This is the familiar circular function expressed by the relationship:

where a and b are arbitrarily chosen constants. A line 60 is drawn through the several tangents of the members of this curve family with lines parallel to the y-axis to effect two groups 61 and 62 of semi-circular curves. The curve group 61 is inscribed on a belt, such as 10 of Fig. 1, in each of frames and in positions corresponding to those occupied by curve groups 15. Similarly, the curve group 62 is plotted on the belt in each of frames 21 in the positions of curve groups'16. "The-operation of the computer is thereafter the same as described hereinbefore.

Fig.' 5 is an example of a family of empirically derived curves, such as usedin contour mapping, that may be accommodated by the computer ofFig. 1. It will be observed that in this case, for selected valu'esof x and a' particular value of z, y may take on four values. Accordingly, three reference lines, 63, 64 and 65, are drawn,- each corresponding to the loci of'tangents'parallel to the y-axis (there are three such loci).- These lines 63--65 are not straight nor are they parallel to the x-axis as in the examples of Figs. 2 and 4; Fig. 5 thus-represents a more general case.

The family of curves is thus divided into four groups,

66, 67, 68 and 69. Groups 66 and 68 are plotted adja-- cent one another in vertically spaced relation on each of successive ones of frames 20 (belt 10 of Fig. 1) and groups 67 and 69 are likewise inscribed adjacent one another in vertically spaced relation on each of frames- 21. Apart from the' manner of positioning the curve groups on the belt, the operation of the computer remains unchanged from that presented earlier.

In Fig. 6 there is shown a modified arrangement employing a moving belt 10a onwhich frames-20a and 21a are distributed in alternation. Frames 20a individually include curve family portion 15a, opaque section 28a and opaque synchronizing strip portion 39a, and frames 21a each comprise curve family portion 16a, opaque section 28a and transparent synchronizing strip portion 40a. To this extent belt 10a is like belt 10 of Fig. '1,

however, it is provided with another synchronizing strip including an opaque section 39a in each of frames 21a and a transparent section 40a in each of frames 20a. Light beams from sources 41a and 41a are directed by lenses 42a and 42a toward synchronizing strips 3911,4011

and 39a, 40a, respectively, and light energy, after modification by the strips, is intercepted by photoelectric cells 43a and 43a.

The photocells 43a and 43a are electrically coupled to amplifiers 31a and 32a which are so biased that they are inoperative in the absence 'of a pulse from the corresponding photocell. The output of another photocell 24a is applied to the input circuit of each of the biased amplifiers. The latter photocell receives light energy of beams 23a and 26a after modulation by curves 15a, 16a and regions 28a of belt 10a.

Pulses from photocells 43a and 43a, corresponding to pulses 52 of Fig. 3B and to pulses 53 of Fig. 3C, respectively, operatively condition amplifiers 31a and 32a in alternation. Thus, pulses produced by curve family portion 15a alone are supplied by amplifier 31a to a corresponding integrator and pulses produced by curves 16a are supplied by amplifier 32a to'the other integrator. Thereafter, the operation of the computer is the same as explained in connection with Fig. 1.

Of course, other types of synchronization may be employed. For example, a generator of electrical pulses may be mechanically driven by motor 14 of Fig. l to provide the control pulses 52 and 53 of Fig. 3.

If it is desired to avoid the use of electronic switches 29 and 30 and the attendant synchronizing apparatus including source 42, photocell 43, amplifier 45 and phase inverter 46, the modified system illustrated in Fig. 7 may be employed. Transparent belt 10b is provided with successive frames and although but one of these frames is shown, it is to be understood that a plurality of identical frames are provided on the endless belt that is driven at a preferably constant velocity.

Frame 80 is comprised of three laterally-spaced sections 81, 82 and 83. In section 81 a group of curves 15b is inscribed as opaque lines, section 82 carries curves 16b and an opaque region 28b is disposed in section 83.

Each of a pair of mirror type galvanometers 84 and 85 is supplied with a voltage having a magnitude responsive to the instantaneous value of variable x and their individually-reflected light beams 86 and 87 are projected toward sections 81 and 82, respectively, of belt 10b. After modulation by curve groups b and 1611 the beams 86 and 87 are intercepted by individual photoelectric cells 88 and 89 and the resulting electrical impulses from the photocells are supplied to biased amplifiers 31b and 32b.

A voltage denoting the instantaneous value of variable y is supplied to a mirror galvanometer 27b and its reflected light beam 26b is modulated by region 2% of belt section 83 before interception by a photocell 90. The output of photocell 90 is applied to each of amplifiers 31b and 32b which operate in the same manner as amplifiers 31 and 32 of Fig. 1.

Accordingly, amplifiers 31b and 32b provide individual sequences of output pulses dependent in number on the instantaneous values of x and y, but representative ol curve groups 15b and 16b','respectively. As in the circuit arrangement of Fig. l, the individual sequences are counted by integrators 33b and 34b and the resulting voltages are subtractively combined in network 35b to produce a voltage, representative of the instantaneous value of 2, that is supplied to indicator 381).

In Fig. 8, there is illustrated one way of obviating the need for individual galvanometers 84 and 85 of the system shown in Fig. 7. A single, mirror galvanometer 91 is employed to reflect light energy from a source of white light 92 and the reflected beam. 93 is positioned relative to a modified belt 10c. Curves 150 are plotted on section 94 of each frame 800 as translucent or transparent lines of green color on a substantially opaque blackground. Similarly, curves 16c are plotted as translucent or transparent lines of red color on an essentially opaque background in section 95 of every frame.

Modulated light in the two colors is directed by a prism 96 to a green filter 97 before interception by photoelectric cell 880 and to a red filter 98 before impinging upon photoelectric cell 89c. The system and electrical circuit, apart from that just-described up to photocells 88c and 89c, is the same as shown in Fig. 7 and need not be redrawn. Obviously, belt section 94 appears to be entirely opaque to photocell 89c and it sees only the lines 160 of section 95. Likewise, section 95 appears entirely opaque to cell 88c which sees only lines 150 of section 94. Therefore, by use of color separation, only a single galvanometer for variable x is required. Moreover, as may be seen in Fig. 8, the entire family of curves 15c, 160 may be plotted on each frame 800, the portions of the family, of course, being appropriately colored.

Of course, other methods for effecting this type of separation may be employed, such as the use of different transmission characteristics. For example, curves 15c may be transparent on an opaque background and a belt section 94 may be coated with a material that polarizes light horizontally. The section 95 is coated with a vertically polarizing material and filters 97 and 98 are of the types producing horizontal and vertical polarization, respectively.

Although curve groups 15c and 160 have been shown as physically separated, if a suitable light separating system is employed, they may be superimposed on one another.

Another arrangement for permitting the use of a single galvanometer in place of the two (34 and 85) shown in Fig. 7 comprises a galvanorneter provided with a pair of vertically displaced mirrors actuated by a common driving element. The mirrors are also angularly displaced so that each of the resulting light beams from a pair of vertically displaced sources may be reflected as an individual one of the beams 86 and 87.

While it may be preferable to displace the moving belts of Figs. 1, 6, 7 or 8 at a constant velocity where time integration of pulses is performed, the respective systems may be modified to relieve this requirement. For example, the belt may be provided with an additional track including equally spaced markings. By means of another photocell-integrator combination associated with the track, a potential may be developed having an amplitude dependent upon the track velocity. This potential may be utilized to control the output of amplifiers, interposed between integrators 33 and 34, for example, and combining circuit 35, in such a manner asto correct for speed variations.

In Fig. 9 of the drawings, there is illustrated an allelectronic computer constructed in accordance with the present invention and embodying features disclosed and claimed'in the aforementioned copending Doll application, Serial Number 359,197, now Patent 'No. 2,859,916. To illustrate its operation, the curve family of Fig. 2 is shown in association with the apparatus.

This computer comprises a pair of cathode ray tubes 100 and 101. Tube 100 includes an electrode system 102 for projecting a focused beam of electrons toward a fluorescent screen 103. The electron beam is under the influence of a pair of horizontal deflection plates 104 and a pair of vertical deflection plates 105 included in a deflection system for controlling the position of the electron beam relative to screen 103. Tube 101 similarly includes an electrode system 106, a deflection system 107, 108 and a fluorescent screen 109.

A deflection voltage having a magnitude dependent upon the instantaneous value of an independent variable x is applied via terminals to the horizontal deflection plates 104 and 107 of cathode ray tubes 100 and 101 and a deflection voltage having a magnitude dependent upon the instantaneous value of independent variable y is applied to the vertical deflection plates 105 and 108 of these tubes via terminals 111.

Also applied to the two sets of vertical deflection plates 105 and 108 is a triangular wave derived in a sweep generator 112. Thus, the electron beams within the tubes 100 and 101 recurrently scan screens 103 and 109 to derive respective recurrent traces of radiant energy in the visible portion of the spectrum. In other words, a line scan or trace is generated on each of the screens and the position of both traces is under the control of the voltage representing variables x and y.

A screen 113 on which curves 114 are inscribed is positioned adjacent screen 103 and similarly a screen 115 carrying curves 116 is disposed adjacent screen 109. In order to determine the extent of each of curve groups 114 and 116, the following procedure may be employed. An entire family of curves is associated with one of the cathode ray tubes, say tube 100, being positioned adjacent the fluorescent screen 103. With sweep generator operating to provide a vertical trace on screen 103, manually controlled voltages are. applied to terminals 110, 111 to position the trace or scan at the several points of tangency with the members of the curve family. The locus of these points defines a reference line to one side of which curve group 114 occurs and having on the other side curve group 116.

A condensing lens 117 gathers the light energy from screen 103, after its modification or modulation into pulses by curve group 114, and directs it toward a photocell 118 connected to a pulse equalizer 119. Stage 119 produces pulses corresponding in timing to those supplied by cell 118 and of constant amplitude and duration. These, uniform or equalized, pulses are counted by an integrator 120. Modified or pulsed light from screen 116 is similarly directed by a lens 121 onto a photocell 122 coupled to another pulse equalizer 123, in turn, coupled to an integrator 124. The outputs of integrators and 124 are subtractively combined in circuit 125 and the resulting potential is indicated at an output device 126, such as a recording voltmeter.

In operation, similar vertical sweep traces are generated on screens 103 and 109' of cathode ray tubes 100 and 101. These traces are simultaneously and continuouslyoriented in two coordinates (horizontal and vertical), ac cording to the instantaneous values of independent variables x and y. Interruptions in the light traces are caused by the curves in groups 114 and 116, respectively; thus, an individual sequence of pulses of light energy for each of the curve groups impinges on the associated one of photocells 118 and 122. The number of light pulses in each sequence is dependent upon the instantaneous Values of variables x and y and the two sequences of electrical pulses are employed to cause pulse equalizers 119 and 123 to produce similar sequences. Accordingly, each of integrators 120 and 124 develops a potential dependent in magnitude upon the instantaneous values of the independent variables, but also individually related to one of the curve groups. These potentials are subtractively combined in circuit 125 thereby deriving a potential representing the instantaneous value of dependent variable z. The latter potential is continuously indicated by device 126 as the computed value of z.

It is evident that by dividing the curve family into two groups and deriving separate signals for each group which may be subtractively combined, errors otherwise arising due to the sweep trace intercepting a curve or curves more than once are avoided.

Obviously, other directions of scanning may be employed according to the configurations of the curve family. For example, with the family just illustrated, a 45 scan may be utilized. This direction of scan may be accomplished by supplying the output of generator 112 to both the horizontal and vertical deflection elements of each cathode ray tube with equal amplitude. Other directions may be achieved by suitably apportioning the horizontal and vertical sweep signals in a known manner.

Of course, if the sweep direction is altered, the reference line delineating the curve groups 114 and 116 usually must be redeterrnined in accordance with thepractice outlined hereinbefore. In any event, the sweep trace should be of essentially constant direction and of a substantially fixed length great enough so that all curves in any group may be intercepted by the sweep trace at a set of values of x and y, where all curves should be cut.

In the modified arrangement shown in Fig. 10, only a single cathode ray tube 130 is required. Although but a portion of this tube, including a fluorescent screen 131 is represented, it is to be understood that it comprises beam forming and deflection systems, and it is supplied with sweep and deflection voltages, for example, as shown for tube 100 of Fig. 9.

A screen 132 inscribed with curve groups 133 and 134 is positioned adjacent fluorescent screen 131. The curve groups 133 and 134 together correspond to the family of curves 17 and 18 of Fig. 2 and the extent of each of these groups is determined by a reference line 135 extending through the locus of sweep traces with the several curves, as explained in connection with the system of Fig. 9.

An opaque, sheet-like light shield 136 extends from line 135 of curve-carrying screen 132 in a direction transverse to the plane of the screen. The light shield 136 is of size suflicient to exclude light modified by the curve group 134 from a lens 137 that concentrates this light on a photocell 138 and to exclude light modified by curve group 133 from a lens 139 that directs light toward a photocell 140. The photocells 138 and 140 may be connected in the circuit of Fig. 9, being susbtituted for photo'- cells 118 and 122, respectively.

It is evident that by use of light shield 136, light pulses from curve groups 133 and 134 may be individually counted in that same manner described in connection with curve groups 114 and 116 of the apparatus shown in Fig. 9.

In the computer illustrated in Fig. 11, there is included a cathode ray tube 150 having the usual beam-forming electrode system 151 for projecting an electron beam to ward a fluorescent viewing screen 152. An electromag- 1'0. ntic deflection system comprised-of horizontal and yertical deflection coils 153 and 154 controls the position of the electron beam relative to screen 152.

A sweep generator 155 supplies a deflection signal to coils 153 and 154 via individual variable gain amplifiers 156 and 157. The amplification of these amplifiers is under the control of voltages at. terminals 158 and 159, having magnitudes dependent upon the instantaneous values of independent variables x and y, respectively. Thus, a sweep trace is developed on fluorescent screen 152 having one extremity always intercepting a point which may be defined as,x=0, 2:0 and its other extremity intercepting another point dependent upon the instantaneous values of independent variables x and y.

A curve-carrying screen 160 comprising portions 161 and 162 is positioned adjacent fluorescent screen 152. Portion 161 is coated with a material which causes the light passing through the screen to be horizontally po larized and portion 162 is coated so as to effect vertical polarization on transmitted light. Light from both portions is directed by a lens 163 toward a pair of photoelectric cells 164 and 165 which may be electrically coupled in place of photocells 118 and 122, respectively, of'Fig.

9. Vertically and horizontally polarized light filters 166 and 167 are interposed between lens 163 and respective ones of photocells 164 and 165. Thus, horizontally polarized light from screen portion 161 is excluded from reaching cell 165, while vertically polarized light from screen section 162 cannot reach cell 164.

The method of determining the extent of screen portions 161 and 162 may be best explained by reference to Fig. 12, illustrating a family of curves 168 plotted in rectangular coordinates, lines 169 and 170 being the horizontal and vertical base lines, respectively. The base or zero lines 169 and 170 intersect at point 171, thereby defining the point x=0, y=0 which corresponds to'the same point in the sweep trace developed on fluorescent screen 152.. A series of radial sweep lines .172 are drawn through point 171 and the points of tangency 173 with the several curves in family 168 are noted. A reference line 174 is drawn through points 173 (line 174 is the locus of tangent points) thereby dividing curve family 168 into two groups. The curve group nearest base lines 169, 170 is disposed in section 161 of screen 160 and the remaining group occupies portion 162 of the screen. Reference line 174, of course, is the dividing line between portions 161 and 162 and determines the extent of the two types of polarization materials employed for the portions.

In operation, the sweep trace on fluorescent screen 152 The two tubes are supplied with identical electrical sig- I nals and a screen including only portion 161 is assoclated with one tube while the other tube is provided with a screen having portion 162. Each tube operates in connection with an individual photocell and light-polarizing filters are not required.

If it is desired to utilize a single cathode ray tube and avoid the use of'polarized or colored filters, the screen may be divided by a diagonal line through x=0, y=0

One curve group is plotted on one side of the line in its usual relation to the point x=0, y=O, and the other group is plotted in mirror image relation with respect to x=0, y=0. Means are provided for periodically switching the radial sweep 180 in phase at a rate much greater than the sweep frequency. Thus, both curve groups may be scanned and a light shield arrangement extending from the diagonal line, for example, as shown in Fig. 10, may be employed.

Although in the several illustrations of apparatus of the moving belt type or of the cathode ray tube variety, embodying the invention, opaque curves on a transparent screen have been shown, it is to be understood that transparent curves on an opaque background may be em ployed. In the former case, the dimension of the light beam in the plane of the screen preferably should be no greater than the width of the curve lines, while in the latter instance, it preferably should be no greater than the spacing between the closest, successive curves.

Alternatively, the screen may be constructed of light reflecting material with the curves on a general background of lesser reflectivity. Thus, reflected pulses of light energy may be delivered to the photoelectric means. Obviously, the curve markings may be applied directly to the outer surface of the screen of the cathode ray tube.

It is evident that a screen including curves inscribed in terms of variations in electron permeability may be disposed Within a cathode ray tube in the electron beam path. A suitable collector electrode may be employed to derive pulses representing the curves intercepting the electron beam scan. One or more cathode ray tubes of this type may obviously be associated in the systems of the type represented in Figs. 9-11 and no photoelectric cells are required. Alternatively, the curves may be plotted of secondary-electron-emitting material.

In Fig. 13, there is illustrated a family of curves exhibiting values of both positive and negative sign. By dividing the family into two groups of curves defined by a reference line 200 coinciding with the O-valued curve, it may be accommodated by an automatic computer embodying the present invention, such as shown in Fig. 14.

This computer, which is generally similar to the one shown in Fig. 6, comprises a transparent, endless belt 201 associated with sprocket wheels 202 and 203, the latter of which is rotated by a driving motor 204. Motor 204 preferably drives the belt at a fixed velocity.

Screen 201 is inscribed with opaque curves occurring in two, alternating groups 205 and 206, corresponding respectively to the members of curve family in Fig. 13 above and below reference line 200. The curve groups 205 and 206 are positioned in respective frame portions 207 and 208 of belt 201 in the same relative positions aswould occur if each pair of complementary groups were disposed in the same frame.

Light energy from a source (not shown) is reflected by a mirror galvanometer 209 and projected in a beam 210 toward the section of belt 201 carrying curves 205 and 206. A voltage having a magnitude proportional to the instantaneous value-of independent variable x is applied to galvanometer 209. Accordingly, the position of beam 210 along a horizontal path transverse to the direction of belt displacement is dependent upon the value of variable x. 3

Light energy from another source (not shown) is reflected in a beam 211 from another mirror galvanometer 212 to which is applied a voltage representing the in stantaneous value of independent variable y. Beam 211 is positioned along a path transverse to belt movement according to the value of variable y, but with relation to a series of opaque sections 213 and 214 of the belt. Each of opaque sections or regions 213 is disposed in one of frames 207 and regions 21tare likewise disposed in frames 208. Regions 213 and 214 have respective configurations permitting counting of a number of the associated ones of curve groups 205 and 206 dependent upon the value of variable y, as may be more apparent in the discussion to follow.

Light energy'in beams 210 and 2 11, after modification or modulation into pulses by the opaque portions of belt 201 is intercepted by anelongated photoelectric cell 215 whose output is supplied to two biased amplifiers 216 and 217. These amplifiers arebiased so that they are inoperative until actuated by gating pulses from respective photoelectric cells 218 and 219. The cells receive light energy from sources 220 and 221 after modulation by individual synchronizing strips 222, 223, and 224, 225 of belt 201. Opaque strip 222 and transparent strip 225 are disposed at opposite sides of frames 20?, and transparent strip 223 and opaque strip 224 are disposed at opposite sides of frames 208. It will be recognized that the foregoing synchronizing arrangement is generally similar to the one shown in Fig. 6.

Amplifiers 2 16 and 217 are so biased that in addition to the gating action just described, each produces output pulses only in response to input pulses representing the curves of groups 205 and 206 that are concurrent with the rectangular pulses resulting from opaque regions 213 and 214. These output signals are supplied to individual integrators 226 and 227 where pulses are counted. The integrators derive potentials that are subtractively combined in a circuit 228 before application to a voltmeter 229. The voltmeter is provided with a scale 230 calibrated to indicate both positive and negative values.

In operation, mirror galvanometers 209 and 2 12 are supplied with voltages having magnitudes dependent upon the instantaneous values of independent variables x and y, respectively, and light beams 210 and 211 are oriented accordingly.

As the curve groups 205 and 206 sweep past light beam 210, a series of short-duration pulses are generated by photocell 215. Simultaneously, corresponding ones of regions 213 and 214 modulate light beam 211, and rectangular pulses are generated by the photocell.

Due to the gating action on amplifiers 2'16 and 217 produced by synchronizing strips 222, 223 and 224, 225 and photocells 218 and 219, amplifier 216 translates pulses derived solely from frames 207 and amplifier 217 translates pulses exclusively from frames 208. It will be recalled that frame 207 is provided with curves of positive value, whereas frame 208 carries curves of negative value. Thus, integrators 226 and 227 derive respective summations for the two groups of curves. The subtractive combination of these summations in circuit 22% results in a potential having a magnitude and polarity rep resentative of the computed value of dependent variable z.

The configurations of opaque regions 213 and 21d of belt 201 may be best understood by considering certain operating conditions. For example, let it be assumed that the instantaneous value of variable x is small and that the instantaneous value of variable y is large to provide a value of z equal to plus 3. To arrive at this re sultant, the apparatus should count the three curves above the reference line 200 of Fig. 13, while counting none below.

To comply with the assumed operating condition. light beam 210 is positioned to the left extremity of the belt section carrying curve groups 205 and 206, whereas light beam 211 is at the right extremity of the portion of the belt carrying regions 213 and 2 14. Thus, the short-duration pulses produced by curves 205 concur with a portion of the rectangular pulse derived in response to region 213. As a result, three pulses are supplied to and counted by integrator 226.

It is evident that three pulses representing curves occur before a relatively short-duration rectangular pulse is produced by region 214. Consequently, no pulses are supplied to integrator 227.

The combination of potentials representing pins 3 and 0 in the circuit 228 effects a scale reading at meter 22? of plus 3 units.

Let it now be assumed that the instantaneous value of x remains unchanged,'*but= that thevalue of y is small so that a z value or minus 3' should be computedu, Light beam 211 thus is oriented at the left extremity of the associated portion of belt 201. Obviously, the relatively short-duration rectangular pulse due to region 213 occurs before the pulses caused by the curves of group 205. Moreover, three: pulses representing curves 206 occur during the long-duration pulse from region 214. Thus, integrator 227 derives a potential representing three pulses, integrator 226 derives none and meter 229 indicates a z value of minus 3;

It is thus evident that the computer of Fig. 14 may accommodate a family of curves having values-of both positive and negative sign. 4

Furthermore, any curve family may obviously be substituted for the one represented in Fig. 13, provided that the family is separated into two groups by a reference line intermediate the positive and negative values and each of the groups is suitably inscribed in the frames 207 and 208 of a belt like the one designated 201. No circuit adjustment is required to permit sucha substitution of curves; it

Although a computer of the type shown in Fig. 14 has been illustrated to accommodate the curve family in Fig. 13, any of the moving belt types represented in Figs. 1, 7 and 8 may be utilized. Of course, the curve family may also be accommodated by any of the cathode ray type computers shown in Figs. 9-11. For example, the curve family under consideration has been shown in association with a cathode ray type computer shown in Fig. 15, generally similar to the one represented in'Fig. 9.

It comprises a pair of cathode ray tubes 250 and 251 having respective pairs of horizontal deflection plates 252, 253 and respective pairs of vertical deflection plates 254, 255 for controlling their individual electron beams projected by electron guns 256, 257 toward fluorescent screens 258, 259. a

the given phase to vertical deflection plates 255 of cathode ray tube 251. p

A transparent screen 263 inscribed with a'group of opaque curves 264, corresponding to those of the curve family of Fig. 14 below reference line 200, is disposed adjacent fluorescent screen 258. Similarly, a transparent screen 265 inscribed with opaque curves 266, corresponding to the curves of Fig. 13 above reference line 200, is positioned adjacent fluorescent screen 259. Light energy after modification by the screens'263 and 265 is directed by lenses 267 and 268 toward respective photoelectric cells 269 and 270. i

The output of photocell 269 is applied to a pulse equalizer 271 whose output is supplied to an integrator 272, in turn, coupled to-a combining circuit 273. The output of photocell 270 is fed to a pulse equalizer 274 coupled to an integrator 275, in turn, coupled to a combining circuit 273. The output of combining circuit 273 is applied to an output meter 276.-

In operation, a vertical sweep trace-is developed on each of fluorescent screens 258 and 259. The position of each of these traces is under the control of the x and y voltages. By reason of the opposite phase relation of the sweep signal at the vertical deflection plates 254 and 255, the trace on screen 258 extends from a point x, y in 'an upward direction and the trace on viewing screen 259 extends from a point x, y in a downwardly direction.

It is evident that a number of light pulses are developed '14 by interruption of the sweep traceby curves 264 representingthe negative'values of z and a number of light pulses aredeveloped asa result of interception of a sweep trace by curves 266 representing the positive values of z. These trains of, light pulses are individually converted to corresponding electrical pulses at photoelectric cells 269' and 270 and after conversion of these pulses to corresponding pulsesrof fixed amplitude and duration in the pulse equalizers, respective potentials are developed by integrators 272 and 275 having magnitudes representative of the numbers of the applied pulses. These potentials are subtractively combined in circuit 273 before application to indicator 276. Thus, accurate indications of the computed value of dependent variable z are afforded by the computer illustrated in Fig. 15.

Obviously, by providing suitably inscribed frames, a curve family exhibiting bothpositive and negative values as well as multiple values of variable y for various values of variable x may be accommodated; In such an arrangement, the features'of the computers of Figs. 6 and 14 or those of the computers illustrated in Figs. 9 and 15 are combined.

While particular embodiments of the present invention have been shown and described, it is apparent that changes and modifications maybe made without departing "from this invention in its broader aspects, and therefore, the aim in the appended claims is to cover all such changes and modifications as fall-within the true spirit and scope of this invention. Y

I claim:

1. Automatic computing apparatus comprising: a family of curves occurring in two groups defined by a reference line; means for projecting radiant energy toward said curves; means for recurrently and relatively displacing said curves and said radiant energy to efiect modulation of said radiant energy; means responsive to said modulation for deriving two electricalsignals, each representing one of said groups of curves; means responsive to each of two independently variable quantities for effectively controlling both of said electrical signals; and means for combining said electrical signals.

2. Automatic computing apparatus comprising: means having a general background area and indicia representing a family of curves occurring in two groups defined by a reference line, said general background area and said indicia having different effects on incident radiant energy; means for projecting radiant energy in at least one beam toward said curves; means for recurrently and relatively displacing said curves and said beam to effect modula tion of said beam; means responsive to said modulation of said beam for deriving two electrical signals, each representing one of said groups of curves; means responsive to each of two independently variable quantities for effectively controlling both of said electrical signals; and means for combining said electrical signals.

3. Automatic computing apparatus comprising: means having a general background area andindicia representing a family of curves occurring in two groups defined by a reference line, said general background area and said indicia having different effects on incident radiant energy; means for projecting radiant energy in at least one beam toward said curves; means for recurrently and relatively displacing said curves and said beam of radiant energy to efiect modulation of said radiant energy into pulsations; means responsive to said modulation of said radiant energy for deriving two pulse-type electrical signals, each representing one of said groups of curves; means responsive to each of two independently variable quantities for effectively controlling both of said electrical signals; means for deriving respective summations of the number of pulses in each of said electrical signals; and means for combining said summations.

4. Automatic computing apparatus comprising: a family of curves occurring in two groups defined by a reference line; means for projecting radiant energy toward said curves; means for 'recurrently and relatively displacing said curves and said radiant energy to effect modulation of said radiant energy; means responsive to said modulation of said radiant energy for deriving two pulse-type electrical signals, each representing one of said groups of curves; means for deriving two potentials, each having an amplitude dependent upon the number of pulses in one of said electrical signals occurring in a given time interval; means responsive to each of two independently variable quantities for effectively controlling both of said electrical signals; and means for indicating an algebraic combination of said potentials.

5. Automatic computing apparatus for determining the value of 'a predetermined function of two independent variables comprising: screen means having'general background area and indicia in the form of a family of curves representing said function and occurring in two groups defined by a reference line, said general background area and said indicia having different effects on incident radiant energy; means for projecting radiant energy in at least one beam toward said screen means; means for recurrently and relatively displacing said screen means and said beam to effect modulation of said radiant energy into pulsations;'means for positioning said beam and said screenmeans with respect'to one another according to the instantaneous value of one of said independent variables; means responsive to said modulation of said radiant energy for deriving two pulse-type electrical signals, each including a number of pulses corresponding to the number of curves in one of said groups of curves intercepted by said beam; means responsive to the remaining of said variables for effectively controlling both of said electrical signals; means for deriving two potentials, each having an amplitude dependent upon the number of pulses in one of said electrical signals occurring in a given time interval; and means for deriving an algebraic combination of said potentials thereby to indicate the instantaneous value of said function.

6. Automatic computing apparatus comprising: a family of curves, means for projecting radiantenergy in at least one beam toward said curves, means for recurrently and relatively displacing said curves and said beam thereby to scan said curves with said radiant energy and effect modulation thereof, said curves occurring in two groups defined by a reference line denoting the locus of tangent points formed by said scan and each of said curves, means responsive to said modulation of said radiant energy for deriving two electrical signals, each representing one of said groups of curves, means responsive to each of two independently variable quantities for effectively controlling both of said electrical signals, and means for combining said electrical signals.

7-. Automatic computing apparatus for utilizing a family of curves defining a function of two independent variables comprising: a screen movable along a predetermined path; means for displacing said screen along said path; means for projecting light energy in at least one beam toward said path; two groups of curves comprised of selected portions of said family of curves and included in said screen so as to have a modifying efiect on said light energy; means for positioning said beam transversely of said path according to the instantaneous value of one of said variables; means for intercepting said beam subsequent to modification by said curves and for deriving two electrical signals, each representing one of said groups of curves; means responsive to the remaining of said variables for effectively controlling both of said electrical signals; and means for combining said electrical signals.

8. Automatic computing apparatus for utilizing a family of curves defining a function of'two independent said screen along said path; meansfor projecting light a energy in a beam toward said path; two groups of curves comprised of selected portions of said family of curves,

included in said screen in alternating order relative to one another and having an effect on incident light energy other than said given, effect so as to cause a modification in light energy of said beam; means for positioning said beam transversely of said path according to the instantaneous value of one of said variables; means for intercepting said beam subsequent to modification by said curves and for deriving a pulse-type electrical signal representing said groups of curves; means operable synchronously with displacement of said screen for separating said electrical signal into first and second pulse-type elec trical signals, each representing one of said groups of curves; means responsive to the instantaneous value of the other of said variables for determining a time interval of utilization of each of said first and second signals; and means for utilizing the portions of said first and said second signals concurrent with said time interval to obtain an indication of the instantaneous value of said function.

9. Automatic computing apparatus for utilizing a famil of curves defining a function of two independent variables comprising: a screen movable along a predetermined path; means for displacing said screen along said path; means for projecting light energy toward said screen in a pair of beams displaced laterally from one another relative to said path; two groups of curves comprised of selected portions of said family of curves, included in said screen in alternating order relative to one another in a direction parallel 'to said path and arranged so as to have a modifying effect on light energy of one of said beams; means for positioning said one beam transversely of said path according to the instantaneous value of one of said variables; a plurality of regions included in said screen, each disposed laterally of one of said groups of curves relative to said path and having a configuration defining a time interval dependent upon the speed of said screen and the instantaneous value of the other of said variables, said regions being arranged to have a'modifying effect on light energy of the other of said beams; means for positioning said other beam transversely of said path according to the instantaneous value of the other of said variables; means for intercepting said beams subsequent to modification by said curves and said regions and for deriving two electrical signals, each including a series of pulses representing one of said groups of curves and occurring during a time interval dependent upon said other variable; and means for utilizing said electrical signals to indicate the instantaneous'value of said function.

10. Automatic computing apparatus for utilizing a family of curves defining a function of two independent variables comprising: a screen movable along a predetermined path; means for displacing said screen along said path; means for projecting light energy toward said screen in a first and a second beam displaced laterally from one another relative to said path; two groups of curves comprised of selected portions of said family of curves, included in said screen in alternating order relative to one another in a direction parallel'to said path and arranged so as to have a modifying effect on light energy of said first beam; synchronizing regions included in said screen, having sections correspondingly positioned with respect to the'curves in one of said groups and arranged so as to have a modifying elfect on lightenergy of said second beam; means for intercepting said first beam subsequent to modification by said curves and for deriving successive trains of electrical pulses, each such train representing the modulation of said first beam by one of said groups of curves; means for intercepting said second beam subsequent to modification by saidsynchronizing regions and for developing a gating signal having-control pulses corresponding in timing with the passing'of one of said groups of curves "past said first beam; means supplied with said successive trains'of electrical pulses and operated by said .17 control pulses for separately deriving the ones of said trains representing one of said groups of curves; and means for utilizing the separately derived trains of electrical pulses to indicate the value of said function.

11. Automatic computing apparatus for utilizing a family of curves defining a function of two independent variables comprising: a screen movable along a predetermined path; means for displacing said screen along said path; means for projecting light energy toward saidpath in first, second and third beams displaced laterally from one another relative to said path; first and second groups of curves, each including a portion of said family of curves defined by a reference line, included in said screen in alternating order relative to one another in a direction parallel to said path and arranged so as to have a modifying effect on light energy of said first beam; two synchronizing strips included in said screen, one having regions disposed correspondingly vwith said first groups of curves and arranged so as to have a modifying effect on light energy of said second beam, and the other having regions disposed correspondingly with said second groups of curves and arranged so as to have a modifying efiect on light energy of said third beam; means for intercepting said first beam subsequent to modification by said curves and for deriving successive trains of electrical pulses, each such train representing the modulation of said first beam by one of said first and said second groups of curves; means for intercepting said second and said third beams subsequent to modification by said synchronizing regions and for developing two gating signals, each having control pulses corresponding in timing with the passing of one of said first and said second groups of curves past said first beam; means supplied with said successive-trains of electrical pulses and operated by said control pulses of said two gating signals for separately deriving the ones of said trains representing one of'said first and saidsecond groups of curves; and means for utilizing the separately derived trains of electrical pulses to indicate the value of said function.

12. Automatic computing apparatus for utilizing a family of curves defining a function of two independent variables comprising: a screen movable along a predetermined path; means for projecting light energy in at least one beam toward said path; means for positioning said beam transversely of said path according to the instantaneous value of one of said variables; means for displacing said screen along said path thereby to scan said screen with light energy along scanning lines parallel to said path; two groups of curves, each including a portion of said family of curves defined by a reference line denoting the locus of tangent points formed by said scanning lines and said curves in said family, and each included in said screen so as to have a modifying effect on said light energy; means for intercepting said beam subsequent to modification by said curves and for deriving two electrical signals, each representing one of said groups of curves; means responsive to the remaining of said variables for effectively controlling both of said electrical signals; and means for combining said electrical signals.

13. Automatic computing apparatus for utilizing a family of curves defining a function of two independent variables comprising: a screen movable along a given path; means for projecting light energy toward said screen in first and second beams laterally displaced from one another with respect to said path; two groups of curves comprised of selected portions of said family, each of said groups being included in said screen so as to have a modifying effect on light energy of one of said first and said second beams; means for displacing said screen along said path to efiect modulation of each of said first and said second beams of light energy by the curves in a corresponding one of said groups; means for positioning said beams transversely of said path according to the instantaneous value of one of said variables; photoelectric means for intercepting each of said beams after said mod- 1218 a ulation to derive respective first and second electrical signals; meansresponsive to the remaining of said variables for effectively controlling-both of said electrical signals; and means for utilizing, said firstc'and said second signals to indicatethe value of said function. t.

14. Automatic computing apparatus for determining the instantaneous value of a function of "two independent variables defined by a family of curves comprising: screen means including a first sectionexhibitinga first effect onincident radiant energy and havinglone. portion of said family of curves, and a second section exhibiting a sec ond effect on incident radiant energy other than said first effect, and having another portion oftsaidfamily of curves; means for projecting radiant energy in a beam toward said screen means; means for; recurrently and relatively displacing said'screen means and said beam to effect modulation of said radiantenergy by said curves;

meansfor positioning said beam and said screen means relative to one another according to instantaneous values of one of said variables; means for intercepting said beam 1 after modulation by saidcurves and sensitive solely to said first effect, to theexclusion, of said second effect, for deriving an electrical signal representing said modulation of said radiant energy by said one portion'of: said family; means forgintercepting'said beam after-modulation by said curves and senitive solely to said second'efffect, to the exclusion of said first effect, for deriving an other electrical signal representing saidmodulation of said radiant energy by said other portionrof said family; means responsive to the remaining of said variables for effectively controlling both of said electrical; signals; and means forutilizing said electrical signals. to indicate the instantaneous value of saidfunction. r, 4 v- 15. Automatic computing apparatus; for'determining the instantaneous value of;a function of two' independent variables defined by va' family of curves comprising: a screen movable along a given-path andincluding first and second sections disposed in alternating relation along said path, said first section'having a portion of said family of curves andefiective to *polarize incident light in one direction, and said second section having another portion of said family of'cu'rves and effective to =polarize in cident light in a different direction substantially trans-I verse to said onedirection; meansfor-projecting a beam of light toward said path'and for positioning said "beam directions to the exclusion of the other direction to de-:

velop two eleotricalsignals, each corresponding to modu'-- lation of said light by curves of said'one of said portions;

means responsive to the remaining of'said variables for effectively controlling both of said electrical signals; and means for utilizing said electrical signals to indicate the instantaneous value of said function. v 16. Automatic computing, apparatus comprising: a fam-' ily of curves occurring in-two groups defined by a refer encelme; cathode ray means including fluorescent screen means and means foriprojecting at'least one beam of electrons toward said screen means to derive light energy projecting toward said curves; a deflection system associated'with said cathode ray means for controlling the position of the point of impingement of said beam of elec trons on said screen means; means for supplying a sweep signal .to said deflection system recurrently to displace said light energy relative tosaid curves to effect modulation of'saidlight energy; means responsive to said m'odu-' lation of said light energy for deriving two electrical sig-' nals, each; representing one of'said groups ofcurves;

means responsive to each of two independently-variable quantities for efiectively controlling both of said electrical signals; and means for combining said electrical signals.

17. Automatic computing apparatus for utilizing a family of curves representing a function of two independent variables comprising: a .pair'of principal screens, each having an individual portion" of said family of curves; a pair of cathode ray tubes, each including a fluorescent screen and means for projecting a beam of electrons toward said fluorescent screen to develop alight beam projecting toward one of said principal screens; a

deflection system-associated with each of said cathode portions of said family; means responsive to the'remaining of said variables for effectively controlling both of said electrical signals; and means for utilizing said electricalsignals to indicate the instantaneous value of said function: l

. 18. Automatic computing apparatus comprising:-' a principal screen having a familyof curves occurring in two groupsdefined by a referenceline; a -ca'tho'd'e ray tube including a fluorescent screen and means for projecting a beam of electrons toward said fluorescentscreen to develop a light beam projecting toward saidprincipal screen; a deflection system associated with saidcathode ray tube for controlling the position of said beam of electrons relative to said fluorescent" screen; a sweep signal source coupled to said deflection system for recurrently sweeping. said beam of-electro'ns thereby to sweep said light beam along a path on said principal screen and effect modulationof said light beaminto pulsations by said curves; a pair of photoelectric devices, each responsive solely to said pulsations of. said light beam-representing one of said groups to the exclusion of said pulsations of said light beam representing the other of said groups; means coupled-to said photoelectric devices for deriving two. electrical signals, each representing one of said groups; means, responsive to each of two independently variable quantities for efiectively controlling both of said electrical signals; and means for combining said electrical signals.

19. Automatic computing apparatus comprising a principal. screen having a family of curves" occurring in two.groups defined. by a reference line; a cathode ray tube including a fluorescent screen and means for projecting a beam of electrons toward said'fiuorescent screen' to develop. a light beam projecting toward said principal screen; a deflection system associated with said cathode ray tube for controlling the position ofsaid beam of elec trons relative to said fluorescent screen; a sweep signal source coupled to said deflection system forrecurrently sweeping said beamof electrons thereby to sweep said light beam along a path on said.principalscreenandeffect modulation of said light beam into pulsations by said curves; a light'shield extending fromsaid reference line'in a direction substantially transverse to the plane ofsaid principal screen; a pair of photoelectric devices, each positioned on a respectiveside of saidlight shield and therebyresponsive solely to said pulsations-of said light beam representing one of said groups to the exclusion of said pulsations ofl said light beam representing the other of; said groups; means coupled to said photoelectric devicesfor deriving twoelectrical signals, each representing oneof-said groups; means responsiveto each of two in- 'two groups definedby a reference line;- a cathode ray tube including a fluorescent screen and means for projecting a beam of electronstoward said fluorescent screen to develop a light beam projecting toward said principal screen; a deflection system associated with said cathode ray tube and including first and second deflection elements operative to control the position of said beam of electrons relative to said fluorescent screen in respective transverse directions; a sweep signal source; a pair of variable-gain signal translating stages, each coupling said source to one of said elements of said deflection system, for supplying electron-beam-deflecting signals to said elements so as to sweep said light beam recurrently along a path on said principal screen dependent upon the gain of said stages, and to efiect modulation of said light beam into pulsations by said curves; means for controlling the gain of each of said stages in accordance with a respective one of two variable quantities; a pair of photoelectric devices, each responsive solely to said pulsations of said light beam representing one of said groups'to the exclusion of said pulsations of said light beam representing the other of said groups; means coupled to said photoelectric devices for deriving two electrical signals, each representing one of said groups; and means for combining said electrical signals.

21. Automatic computing apparatus comprising: a family of curves assigned positive and negative values and occurring in two groups defined by a reference line separating the ones of 'said curves of positive values from the others of said curves of negative values; means for projecting radiant energy toward said curves; means for recurrently said relatively displacing said curves and said radiant energy to effect modulation of said radiant energy; means responsive to said modulation of said radiant energy for deriving two electrical signals, each representing one of said groups of curves; means responsive to each of two independently variable quantities for effectively controlling both of said electrical signals; and means for combining said electrical signals.

22. Automatic computing apparatus for determining the value of a function of two independent variables defined by a family of curves assigned positive and negative values comprising: a screen having said family of curves occurring in two groups, each-such group including curves assigned one of said positive and said negative values; means for projecting radiant energy in at least one beam toward said curves; means for recurrently displacing said screen to efiect modulation of said radiant energy by said curves; means for positioning said beam in a direction transverse to movement of said screen according to in stantaneous values of one of said variables; means responsive to said modulation of said beam for deriving two pulse-type electrical signals, each representing one of said groups of curves; means responsive to movement of said screen and to the instantaneous value of the other of said variables for establishing first and second time intervals for utilization of each of said electrical signals; and means responsive to a time -divided portion of each of said two electrical signals concurrent with one of said 'time intervals for producing indications of the instantaneous value of said function.

23. Automatic computing apparatus for determining the value of a function of two independent variables defined by a family of curves assigned positive and negative values comprising: a screen having said family of curves occurring in two groups, each such group including curves assigned one of said positive and said negative values and having regions of two types, each such type positioned adjacent one of said groups and having a configuration adapted to define a time interval dependent in length upon the speed of movement of said screen and the position of an incident beam of light relative thereto; means for projecting a first light beam toward said curves and for projecting a second light beam toward said regions; means for recurrentlydisplacing said screen to effect modulation of said beams by said curves and by said regions, respectively; means for positioning each of said beams in a direction transverse to movement of said screen according to instantaneous values of a respective one of said variables; means responsive to said modulation of said first beam for deriving two pulse-type electrical signals, each representing one of said groups of curves; means responsive to said modulation of said second beam for deriving two control pulse signals each representing one of said types of regions; means responsive to each of said electrical signals and to the corresponding one of said control pulses for deriving two electrical signals representing said groups; and means for utilizing said electrical signals to indicate the instantaneous value of said function.

24. Automatic computing apparatus for determining the value of a function of two independent ,variables defined by a family of curves assigned positive and negative ranges of values comprising: principal screen means having a family of curves occurring in two groups defined by a reference line, each such group including curves assigned one of said positive and said negative ranges of values; cathode ray means including fluorescent screen means and means for projecting at least one beam of electrons toward said fluorescent screen means to derive radiant energy projecting toward said principal screen means; a deflection system associated with said cathode ray means for controlling the position of said beam of electrons relative to said fluorescent screen means; means for supplying a sweep signal to said deflection system recurrently to displace said beam of electrons thereby to scan said principal screen means with said radiant energy to effect modulation thereof; means coupled to said deflection system for controlling the position of said electron beam and said radiant energy according to instantaneous values of one of said variables; means responsive to said modulation of said radiant energy for deriving two electrical signals, each representing one of said groups of curves; means responsive to the remaining of said variables for eflfectively controlling both of said electrical signals; and means for utilizing said electrical signals to indicate the instantaneous value of said function.

25. Automatic computing apparatus for determining the value of a function of two independent variables defined by a family of curves assigned positive and negative ranges of values comprising: first and second principal screens individually including one of two groups of said curves, each such group including curves assigned one of said negative and said positive ranges of values; first and second cathode ray tubes each including a fluorescent screen and means for projecting a beam of electrons toward said fluorescent screen to derive a beam of light projecting toward a corresponding one of said first and second principal screens; first and second deflection systems associated with corresponding ones of said cathode ray tubes; a source of sweep signals similarly coupled to each of said deflection systems, but phased to sweep the electron beams of said tubes in opposite directions relative to said groups of said family of curves; means coupled to said first and said second deflection systems for positioning said electron beams according to the instantaneous values of both of said variables; first and second photoelectric devices for intercepting light energy after modulation into pulses by a corresponding one of said first and said second principal screens and for deriving respective electrical signals; and means for utilizing said electrical signals to indicate the instantaneous value of said function.

References Cited in the file of this patent UNITED STATES PATENTS 2,139,295 Woodling Dec. 6, 1938 2,428,990 Rajchman Oct. 14, 1947 2,462,263 Haynes Feb. 22, 1949 2,463,362 Doll Mar. 1, 1949 2,497,042 Doll Feb. 7, 1950 2,580,741 Dickinson Jan. 1, 1952 2,670,654 Norman Mar. 2, 1954 

